In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model that now inc
ludes unreliable links controlled by an adversary. We begin by proving that a natural geographic constraint on the network topology is required to solve these problems efficiently (i.e., in time polylogarthmic in the network size). We then prove the importance of the assumption that nodes are provided advance knowledge of their reliable neighbors (i.e, neighbors connected by reliable links). Combined, these results answer an open question by proving that the efficient MIS and CDS algorithms from [Censor-Hillel, PODC 2011] are optimal with respect to their dual graph model assumptions. They also provide insight into what properties of an unreliable network enable efficient local computation.
Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among an unknown
set of nodes) and broadcast (message dissemination through an unknown network topology). In this paper, we introduce a new technique for proving this type of bound, based on reduction from a probabilistic hitting game, that simplifies and strengthens much of this existing work. In more detail, in this single paper we prove new expected time and high probability lower bounds for wake-up and global broadcast in single and multichann
In this paper, we study distributed consensus in the radio network setting. We produce new upper and lower bounds for this problem in an abstract MAC layer model that captures the key guarantees provided by most wireless MAC layers. In more detail, w
e first generalize the well-known impossibility of deterministic consensus with a single crash failure [FLP 1895] from the asynchronous message passing model to our wireless setting. Proceeding under the assumption of no faults, we then investigate the amount of network knowledge required to solve consensus in our model---an important question given that these networks are often deployed in an ad hoc manner. We prove consensus is impossible without unique ids or without knowledge of network size (in multihop topologies). We also prove a lower bound on optimal time complexity. We then match these lower bounds with a pair of new deterministic consensus algorithms---one for single hop topologies and one for multihop topologies---providing a comprehensive characterization of the consensus problem in the wireless setting. From a theoretical perspective, our results shed new insight into the role of network information and the power of MAC layer abstractions in solving distributed consensus. From a practical perspective, given the level of abstraction used by our model, our upper bounds can be easily implemented in real wireless devices on existing MAC layers while preserving their correctness guarantees---facilitating the development of wireless distributed systems.
